Implications of maximal Jarlskog invariant and maximal CP violation

Details Implications of maximal Jarlskog invariant and maximal CP violation Implications of maximal Jarlskog invariant and maximal CP violation

2001-04-10

arxiv.org/abs/hep-ph/0104092v1

Physics

High Energy Physics

High Energy Physics - Phenomenology

25 pages, 3 figures, revtex

Scientific paper

We argue here why CP violating phase Phi in the quark mixing matrix is maximal, that is, Phi=90 degrees. In the Standard Model CP violation is related to the Jarlskog invariant J, which can be obtained from non commuting Hermitian mass matrices. In this article we derive the conditions to have Hermitian mass matrices which give maximal Jarlskog invariant J and maximal CP violating phase Phi. We find that all squared moduli of the quark mixing elements have a singular point when the CP violation phase Phi takes the value Phi=90 degrees. This special feature of the Jarlskog invariant J and the quark mixing matrix is a clear and precise indication that CP violating Phase Phi is maximal in order to let nature treat democratically all of the quark mixing matrix moduli.

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